If everyone updates, then there isn't a longstanding chain split (e.g. https://en.bitcoin.it/wiki/Value_overflow_incident).
But yeah if there's longstanding disagreement, there are two ways for it to go:
* Peaceable fork with replay protection, like Bitcoin Cash
* Fork that seriously fights for the same brand/userbase --- we haven't seen one of these in Bitcoin. Segwit2x would've worked that way, but was canceled